THE CARTESIAN COORDINATE SYSTEM AND GRAPHS OF LINEAR EQUATIONS

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UNIT 16

• THE CARTESIAN COORDINATE SYSTEM AND GRAPHS OF
  LINEAR EQUATIONS

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GRAPHING A LINEAR EQUATION

• The graph of a straight line (linear) equation
  has an infinite number of ordered pairs of
  numbers that satisfy the equation
• Procedure for graphing an equation1. Write the
  equation in terms of either variable (x or y)2.
  a. Make a table of values. Head one column x and
  the other column y b. Select a least three
  convenient values for one variable and find
  their corresponding values for the second
  variable by substituting the first
  variable values in the equation3. Draw a label
  the x axis and the y axis on the graph4. Plot
  the coordinates on the graph5. Connect the
  points. The straight line is the graph of the
  equation

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GRAPHING EXAMPLE

• Graph the equation 2x y 5
• Write the equation in terms of x or y.We will
  use y
• Make a table of values that satisfy the equation
  by choosing a value for x and finding the
  corresponding y value
• Draw and label the x axis and y axis. We will
  show this on the next slide
• Plot the points on the graph. Shown on the next
  slide
• Connect the points as shown on the next slide

y 2x 5
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EXAMPLE GRAPH

• This slide shows the graph of the equation 2x y
  5 from the previous slide

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SLOPE OF A LINEAR EQUATION

• The slope of a linear equation (a straight line)
  refers to its steepness or inclination
• Slope is defined as follows
• If a line rises moving from left to right, it has
  a positive slope
• If a line falls moving from left to right, it has
  a negative slope
• A horizontal line has a zero slope
• A vertical line has an infinite slope

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DETERMINING SLOPE

• Determine the slope of the line that passes
  through the points (1,3) and (1,2)
• Determine the slope of the line that passes
  through the points (2,4) and (3,3)

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SLOPE-INTERCEPT FORM

• If the slope and the y-intercept of a straight
  line are known, the equation of the line can
  easily be determined
• The y-intercept is the y-coordinate where the
  line intercepts (crosses) the y axis the value
  of the x is 0 at this point
• The general equation for the slope-intercept of a
  straight line is y mx b, where m is the
  slope and b is the y-intercept
• Determine the equation of the line given that the
  slope is 2 and the y intercept is 5
• We were given m 2 and b 5 so substitute them
  into the slope-intercept form y mx b
  becomes y 2x 5 Ans

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DETERMINING THE EQUATION OF A LINE GIVEN TWO
POINTS

• If two points on a straight line are known, an
  equation can be determined by finding the slope
  of the line and then finding the y-intercept
• An example of determining the equation of a line
  given two points is given on the next slide

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EXAMPLE OF DETERMINING THE EQUATION OF THE LINE

• Find the equation of a straight line that passes
  through (1,9) and (2,3).
• Find the slope
• Find the y-intercept. Use either point since
  they both lie on the lineUsing the point (1,9)
  and m 2, substitute them into the
  slope-intercept form to find the y-intercept
• Now, substitute the slope and y-intercept into
  the slope-intercept form

y mx b becomes 9 2(1) b which simplifies
to b 7
y 2x 7 Ans
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PRACTICE PROBLEMS

• Graph the linear equations for problems 1 2 by
  plotting points
• 1. 2x y 6
• 2. 6x 3y 15
• Determine the slope of the lines that pass
  through the points given in problems 3 4
• 3. (2, 3) and (4,5)
• 4. (5, 7) and (3, 2)

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PRACTICE PROBLEMS

• Write the equation of the line for problems 5 6
  given the slope (m) and the y intercept (b)
• 5. m 2 b 1
• 6. m 2/3 b 4
• Find the equation for each of the lines passing
  through the points given in problems 7 8
• 7. (1,4) and (3,6)
• 8. (0, 6) and (10, 2)

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PROBLEM ANSWER KEY

• 1. 2.

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PROBLEM ANSWER KEY

• 3. 4/3
• 4. 5/8
• 5. y 2x 1
• 6. y 2/3x 4
• 7. y x 9/2
• 8. y 2/5x 6